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Genetic Algorithms assisted ESATAN Modelling for automatic test verification
and other scientific uses of ESATAN modeling at DLR Berlin
19th European Workshop on Thermal and ECLS SoftwareNoordwijk, 11th-12th October 2005
Riccardo Nadalini
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Summary
� Thermal Probes overview� The inversion Problem� Inversion by Modelling� Parameter search with Genetic Algorithms� Details of the process� Other scientific uses of ESATAN� Ongoing and Future Developments
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Thermal Properties ProbesVarious probes for heat-related experiments are under study:
� MUPUS (Rosetta Lander)
� Extase (terrestrial applications)
� HP3 (planetary and asteroidal heat flow and thermal physics)
All share common characteristics� Shape (long thin “rods”)
� Condition (surrounded by investigated material)
� Operation mode (temperature monitored while heating and cooling of the material occurs)
� Aim (measure of T and thermal properties)
Extase and MUPUS (GRM) probes
HP3 thermal measurements concept
Soil
Surface
Mole
Sensor/Heater
Tether
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InversionTo get the desired information (Cp, k) from a measurement an inversion is required. Two possibilities exist:� Analytical (or direct), by use of heat transfer equations
� Low resources
� Well designed for ideal cases, very difficult to deal with losses and disturbances
� Numerical, by simulation of the experiment with a thermal model
� Model verification needed
� Requires modeller and computation time
Example of measurement (Extase)
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Thermal Modelling (1)
Model characteristics:� Bi-dimensional (axial symmetry)� Parameters included as nodal properties:
� Density (variable)� Cp (constant)� Conductivity (variable)� Contact resistance
(constant)� Depth� Axial distance
Sensors (16)
16 “sensor” layers
Glass Fibre
Foam (insulation)
Kapton layer (sensors)
Probe
Upper boundary layer
Lower boundary layer
10 concentric rings
1
2
…
15
16
……
Purpose: simulate experiments with a certain combination of physical characteristics. If simulation fits the experimental reality, the characteristics of the material (Cp, l,r, Gsurf) are determined
MUPUS-Extase 2D thermal model
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Thermal Model (2)
Results of first Phases� Model vs. experiment, Manual Fit (3 layers)� Satisfactory fit
10
15
20
25
30
35
0 200 400 600 800 1000 1200 1400 1600
Time (s)
Tem
per
atu
re (°
C)
Experiment, Layer 7
Model, layer 7
Exp.layer 8 (below)
Model, layer 8 (below)
Exp. layer 6 (above)
Model, layer 6 (above)
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Open Issues
Even if the thermal model approach proves effective, some outstanding issues remain with a manual fit approach:� No certainty that the solution is optimal and unique� Extremely long and tedious procedure (trial and error) to
find the “right” set of parameters� Limited number of parameters (no more than 4-5)
Necessity of automating the process
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Genetic Algorithms
Disadvantages
� Complex to implement
� Computation intensive
Advantages� Automatic� Reach Optimal solution� Allows tens of parameters
Genetic algorithms are the best known method to create original set of parameters, to be then used in thermal models GA mimic biology:
� Parameter = gene� Set of parameters = chromosome
� Fit to environment = error fit
� Survival of the most fit = selection of the smallest error
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GA fitness
� The median fitness increases quickly at first but slows down approaching the optimum
� The complete parameter space is explored, no local optimum limitation (as per gradient method)
� CPU time for GA (mutation, crossover, selection) depends on parameter set characteristic.
� The error function must be accurately selected
Genetic Algorithms fitness evolution example: individual model fitness (black), population median
(red)
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GA and thermal modelling
Thermal model
Error Evaluation
(GA) Tournament
selection
(GA) Mutation, Crossover
Esatan (fortran) Matlab
Experiment Properties
Numerical Model
Fitness Evaluation
Thermal Layering Data
SimulationData Set
Properties
Genetic Algorithms
ModuleErrorParameters
Experiment
A recursive process is implemented between the model (with an internal error function between simulation and experiment) and the Genetic Algorithms Module
At the programming level, the error evaluation is implemented INSIDE the ESATAN model, while the GA module is in MATLAB.
The two programs exchange data through ASCII text files
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Scientific Uses of ESATAN
In addition to evaluation of experiments, additional scientific simulations are run at DLR Berlin
� Environmental definition � Orbiter-mounted instruments (e.g. Bepi-Colombo Laser
Altimeter)� Surface and subsurface probes (HP3, IR radiometry)
� Scientific Simulation� Mercury surface conditions� Mars subsurface conditions� Mars subsurface long term (climate) simulations� Asteroid surface and subsurface simulations
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Mercury Soil Model (1)
1D soil model (purely conductive, no ESARAD)Parameters included as nodal properties:� Physical parameters (r,Cp, conductivity)� Radiative transmission factor� Location (longitude, latitude) and surface inclination� Node geometric dimensionsSolar flux is calculated directly in ESATAN (Fortran)� Orbit and rotation dependent� Solar disk effect
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Mercury Soil Model (2)
� Stability over 1 cycle (for Mercury 1 solar day = 176 Earth days) is obtained automatically by using SOLCYC� Stability is ~0.001K
� Conditions over entire planet are obtained with a REPEAT … UNTIL cycle calling the solution routine with different parameters
� Results are stored in custom files� Custom ASCII files are also used to store conditions in
case of an interruption� 1 global map of Mercury Temperature (0 to 6m depth,
5°x5° grid, over 1 solar day) is obtained in 30-36 hours of calculation.
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Temperature Curves
0,0
0,5
1,0
1,5
2,0-150 -100 -50 0 50 100
Temperature (°C)
Dep
th (
m)
Midnight 8,8 Days before Sunrise 7,0 Days before Sunrise 3,5
Sunrise 1,8 3,5 5,3
7,0 Days after Sunrise 10,6 14,1 Days after Sunrise 17,6
Midday 61,6 Days after Sunrise 79,2 Days after Sunrise Sunset
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Temperature Maps
Global Result� 1 hemisphere� Temperature at
3m depth� Relevant contours
� Cold (~233K)
� Hot (~313K)
� “Asymmetric” conditions due to Mercury orbit/rotation
� Some mild regions to be found
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Mars Models
To deal with the Mars case, an expansion of the Mercury Soil Model is required, and many modifications must be added:
� Humidity and Volatile contents parameters� Two phase behaviour (condensation and sublimation of
H2O and CO2 ices)� Interaction with atmosphere� Boundary condition come from Mars climate database,
not from internal calculations� Higher Spatial resolution
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Ongoing & future developments (1)
IN the Genetic Algorithms assisted modelling field, the following activities are or will be addressed:
� Implementation of different models
� Recoding of Genetic Algorithms from Matlab to Fortran
� Alternative languages for thermal models (FEM based, Femlab, MATLAB)
� Additional thermal models
� Investigation on the possible use of the Genetic Algorithms approach also for automatic verification of engineering tests (e.g. STM tests, material tests)
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In the scientific applications field the following actions are
or will be implemented
� Implementation of Mars models
� Extended sensitivity analyses on Mercury
surface/underground relations
� Investigation on parallelization
� Solution of licensing issues
Ongoing & future developments (2)
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Acknowledgments
The work has been possible thanks to the help of:Dr. Martin Knapmeyer (DLR Berlin) for the Genetic
AlgorithmsMs. Kathrin Schröer (University of Münster) for the
experimental parts